The properties of quantum systems interacting with their environment, commonly called open quantum systems, can be affected strongly by this interaction. Although this can lead to unwanted consequences, such as causing decoherence in qubits used for quantum computation, it can also be exploited as a probe of the environment. For example, magnetic resonance imaging is based on the dependence of the spin relaxation times of protons in water molecules in a host's tissue. Here we show that the excitation energy of a single spin, which is determined by magnetocrystalline anisotropy and controls its stability and suitability for use in magnetic data-storage devices, can be modified by varying the exchange coupling of the spin to a nearby conductive electrode. Using scanning tunnelling microscopy and spectroscopy, we observe variations up to a factor of two of the spin excitation energies of individual atoms as the strength of the spin's coupling to the surrounding electronic bath changes. These observations, combined with calculations, show that exchange coupling can strongly modify the magnetic anisotropy. This system is thus one of the few open quantum systems in which the energy levels, and not just the excited-state lifetimes, can be renormalized controllably. Furthermore, we demonstrate that the magnetocrystalline anisotropy, a property normally determined by the local structure around a spin, can be tuned electronically. These effects may play a significant role in the development of spintronic devices in which an individual magnetic atom or molecule is coupled to conducting leads.

Iron, cobalt and nickel are archetypal ferromagnetic metals. In bulk, electronic conduction in these materials takes place mainly through the s and p electrons, whereas the magnetic moments are mostly in the narrow d-electron bands, where they tend to align. This general picture may change at the nanoscale because electrons at the surfaces of materials experience interactions that differ from those in the bulk. Here we show direct evidence for such changes: electronic transport in atomic-scale contacts of pure ferromagnets (iron, cobalt and nickel), despite their strong bulk ferromagnetism, unexpectedly reveal Kondo physics, that is, the screening of local magnetic moments by the conduction electrons below a characteristic temperature 1 . The Kondo effect creates a sharp resonance at the Fermi energy, affecting the electrical properties of the system;this appears as a Fano-Kondo resonance 2 in the conductance characteristics as observed in other artificial nanostructures 3,4,5,6,7,8,9,10,11 . The study of hundreds of contacts shows material-dependent lognormal distributions of the resonance width that arise naturally from Kondo theory 12 . These resonances broaden and disappear with increasing temperature, also as in standard Kondo systems 4,5,6,7 . Our observations, supported by calculations, imply that coordination changes can significantly modify magnetism at the nanoscale. Therefore, in addition to standard micromagnetic physics, strong electronic correlations along with atomic-scale geometry need to be considered when investigating the magnetic properties of magnetic nanostructures.Atomic-scale contacts can be fabricated by techniques such as scanning tunnelling microscopy 13 or the use of electromigrated break junctions (EBJs) 14 , where the size of a macroscopic contact between two leads is reduced until they are in contact through only a few atoms and, eventually, through only one. The conductance of metallic monatomic contacts is known to be around 2G 0 , where G 0 = e 2 /h is the spin-resolved quantum of conductance 13 (e being the elementary charge and h Planck ′ s constant). To identify the atomic contacts, histograms are constructed from the evolution of the conductance recorded during the breaking of different contacts (Fig. 1a, b). The position of the first peak of these histograms is identified as the conductance of the monatomic contact. For iron, cobalt and nickel, the conductance is larger than 2G 0 owing to the contribution of the sp and d orbitals to the transmission 15,16,17 .We have studied the low-temperature conductance characteristics of hundreds of atomic-scale contacts of the three transition-metal ferromagnets iron, cobalt and nickel using a home-built STM. More than the 80% of the differential conductance (dI/dV ) curves at the monatomic contact show peaks or dips around zero bias such as those shown in Fig. 1c, which are very similar to those observed in STM spectroscopy of single magnetic adatoms on non-magnetic surfaces 9,10,11 . Thus, as in the case of these Kondo systems, we ca...

Fractionalization is a phenomenon in which strong interactions in a quantum system drive the emergence of excitations with quantum numbers that are absent in the building blocks.Outstanding examples are excitations with charge e/3 in the fractional quantum Hall effect 1,2 , solitons in one-dimensional conducting polymers 3,4 and Majorana states in topological superconductors 5 . Fractionalization is also predicted to manifest itself in lowdimensional quantum magnets, such as one-dimensional antiferromagnetic S = 1 chains.

We study the effect of a structural nanoconstriction on the coherent transport properties of otherwise ideal zigzag-edged infinitely long graphene ribbons. The electronic structure is calculated with the standard oneorbital tight-binding model and the linear conductance is obtained using the Landauer formula. We find that, since the zero-bias current is carried in the bulk of the ribbon, this is very robust with respect to a variety of constriction geometries and edge defects. In contrast, the curve of zero-bias conductance versus gate voltage departs from the ͑2n +1͒e 2 / h staircase of the ideal case as soon as a single atom is removed from the sample. We also find that wedge-shaped constrictions can present nonconducting states fully localized in the constriction close to the Fermi energy. The interest of these localized states in regards to the formation of quantum dots in graphene is discussed.